It seems to be best practice to group related resources in common namespaces, for instance all resources with URI reference starting with http://dbpedia.org/resource/ belong to DBPedia and all classes and properties in an ontology have an URI Reference that starts with the same prefix, for instance http://purl.org/ontology/mo/. Do these patterns carry any semantics except convenience for human readers? If RDF is not made for human readers but for computers, would it make any difference to replace all URI references with a unique hash value?

Which semantic Web technologies rely on the character sequence of URI references apart from equality checks? In theory two URI references are either equal or not but not comparable in any other way such as substring patterns, aren't they? If this is true, where is this rule violated in practice?

Do have a look at Linked Data patterns at http://patterns.dataincubator.org/book/. The Identifier Patterns chapter will give you some ideas on how to create URIs and why they suggest that way. Hope that helps

Do these patterns carry any semantics except convenience for human readers?

No, they don't carry any formal semantics, except for human readers.

If RDF is not made for human readers but for computers, would it make any difference to replace all URI references with a unique hash value?

For computer programmes, it wouldn't make any difference. But human readable identifiers are as much important as choosing human readable names for programme variables. They help people understanding what the content is about. Certainly, the end user will never see the names of the variables or the URIs of things, but there are always various people manipulating the raw data behind the application interfaces.

Which semantic Web technologies rely on the character sequence of URI references apart from equality checks?

The actual sequence is used by protocoles if you ever want to dereference the URIs. http:// indicates the HTTP protocole, dbpedia.org points to the machine where the resource is, /resource/ indicate to the server the file or directory that needs to be thrown back. Apart from this, programmes shouldn't assume anything from the form of the URI.

In theory two URI references are either equal or not but not comparable in any other way such as substring patterns, aren't they?

You MAY use substring comparison for various reasons, one of which is to check that URIs are following best practices, e.g., by using the same namespace for terms of the same ontology. But whatever the practice, good or bad, you should'nt draw conclusions on the meaning of those URIs.

When you say "semantics" I guess it is open to interpretation. The URI string does not have an effective semantics on a standard RDF/RDFS/OWL/SPARQL level, no. But I would argue that there is a whole standard dedicated to providing URIs with semantics (in combination with HTTP, which, for URIs, is kind of analogous to the interpretations used in RDF/OWL semantics): Architecture of the World Wide Web, Volume One.

Some example semantics associated with the syntax of a URI:

A mapping from URIs to representations

What scheme/protocol is associated with the URI

Is the URI strictly an information resource, or can it be a more general form of resource (e.g., has a fragment)?

What is the naming authority of that URI? Do URI A and URI B have the same naming authority?

...

These semantics are specific to the URI string itself and feed directly into Linked Data guidelines and best practices.

Which semantic Web technologies rely on the character sequence of URI references apart from equality checks?

Roughly speaking, anything that uses HTTP. Other non-trivial uses include systems that examine the authority of URIs when dealing with Web data; as a quick example: